In our application Ser. No. 07/922610, we point out that, based on computer modeling and experimental testing of bicycle frames, by strategically reducing tile tube wall stiffness of certain regions within a bicycle frame, the fatigue life of the entire structure can actually be improved. This improvement can be accomplished with little or no added weight to the structure. The reason this is possible is that the peak stresses in a conventional bicycle frame tend to be very concentrated at and near the joints. By locally altering the frame structure, the magnitude of these stresses can be reduced by spreading the loads more uniformly over a larger region of the structure. The result is lower peak stresses and improved fatigue life for the frame. This provided an improved method for reinforcing the access points for cable routing in bicycle frames. In addition, the tubular frame structure exhibits improved strain energy adsorption due to the tube wall modification. The frame will deflect further under a given load, thus adsorbing more impact energy from an impact without failure. This generally improves the safety of the product. That invention redistributed stress near joints in a bicycle frame; provided improved control cable entry/exit points in a bicycle frame; provided improved control cable entry/exit points which are free of welding or brazing to produce a strategically reduced stiffness zone in the structure so as to reduce peak stresses in a bicycle frame and thereby improve the fatigue life of the frame; provided improved control cable entry/exit structures without welding or brazing and without introducing local stress risers in the structural tubing walls of the bicycle frame; provided control cable entry/exit points for tubular members which are framed to produce a bulged, curved or raised surface on the circumference of the tube; and provided an insert, preferably made of plastic or low friction material for the purposes of weather sealing control cable entry/exit apertures, reduce cable friction and improve the aesthetic appearances and appeal of the cable entry/exit structure.